What are some good retro books on mathematics-focused programming?
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MellowCedar47
I'm looking for programming books from roughly the 1970s through the 1980s, or the very early 1990s at the latest, with a strong focus on mathematics and practical algorithms. I'm especially interested in old-school approaches to topics such as numerical methods, discrete mathematics, computation theory, floating-point representation, binary systems, and related problems. I've been searching digital archives, but many useful books have surprisingly obscure or indirect titles. I'm also building an implementation of an older mathematics-oriented programming language and would love problem sets or algorithms to recreate in it, purely as a hobby. What books, journals, or series should I look for?
Answers
The classic recommendation is Numerical Recipes, especially the 1986 edition by Press and Flannery. It was developed in FORTRAN, and it presents the algorithms alongside the equations, so you get a very direct view of how the mathematics becomes working code. Mathematical Methods for Digital Computers by Ralston is another worthwhile older reference, with algorithms intended for practical computer implementation. Searching catalogs for combinations like “numerical analysis” and “programming” may turn up more relevant material than searching for programming books alone.
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It may help to narrow the search by subject, since discrete mathematics, numerical analysis, and computation theory tend to be covered in very different books. If you’re open to all of them, try building a list around classic numerical analysis texts, algorithm collections, computer arithmetic, and mathematical programming languages. That should produce better results than searching for “mathematics programming” as one broad category.
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Knuth’s The Art of Computer Programming is essential if you want rigorous, old-school treatments of algorithms and the mathematics behind them. It can be demanding, but it covers the details exceptionally well and is useful as a long-term reference rather than something to read straight through.
MellowCedar47: I already have the series, although I haven’t worked through it yet. It definitely seems like the kind of reference I’ll keep coming back to.
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Older computer magazines and technical book series may be useful too. Look for material covering floating-point formats, binary arithmetic, numerical algorithms, CRCs, and low-level implementations. Publications aimed at embedded systems often included practical numerical routines, while older Byte-style collections sometimes gathered articles on circuits, algorithms, and computer representation. These can be harder to locate because the relevant material may be filed under hardware or electronics rather than mathematics.
MellowCedar47: That’s a good lead. I’ll look through archives of older computer and embedded-systems publications, especially for numerical routines and representation details.
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Since you’re implementing an older mathematics-oriented language, algorithm collections from the period could be especially valuable. Numerical methods, polynomial and matrix routines, random-number generation, sorting, parsing, and number-theory exercises would all make good test problems while giving you a feel for how programmers worked with limited hardware and memory.
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MellowCedar47: Thanks! I’ve added both of those to my list and will look for copies.